Segregation: The role of race, income and the housing market.

1. Segregation: The role of race, income and the housing market. Alan Kirman, GREQAM,EHESS, Université d’Aix Marseille lll Dejan Vinković IAS Princeton, USA University of Split, Croatia Leiden October 2007

2. A Few Preliminary Comments • This paper takes a model of such a social and economic phenomenon, segregation, and uses a physical analogy to understand it. • Economics has used a model based on classical mechanics. Now more mathematics than physics. • Can different physical models shed light on economic phenomena? • The problem of intention: the man and the stone. • We can sometimes see structure which we would not have found without the physical analogy. • This particular problem.

3. Three steps: racial segregation, income grouping, the housing market. • First I shall give you a rapid view of Schelling’s basic model • Next I will introduce preferences for income group • Then I will introduce the housing market and some variations on the basic model.

4. Isaac Newton « I can calculate the motion of heavenly bodies, but not the madness of people »

5. « A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it » Max Planck, A Scientific Autobiography (1949).

6. What is Schelling’s Basic Model? • People of two different colours live on a chessboard. There are some free squares. • Their utility depends on the number of their neighbours who are of their colour. If a strict majority of their neighbours are of the other colour they are unhappy, low utility, high energy in the analogy.

7. Schelling’s Model: Why is it so famous? • It is intellectually intriguing, emergence of aggregate phenomenon, difficult to predict from individual behaviour. • It is about an important social phenomenon, segregation. • It is easy to explain and play with.

8. Schelling Model • position particles randomly • calculate their utility\energy • create the list of particles that want to move • pick randomly one particle from the list • move it • update the list ? ? Basic rule: move to the nearest empty spot where the utility increases • Variations to the basic rule: • swapping particles • no limit on moving distance • moving when the utility does not change ("liquid", "solid")

18. A Physical Analogue • In the Schelling model utility depends on the number of like and unlike neighbors. In the particle analogue the internal energy depends on the local concentration (number density) of like or unlike particles. • This analogue is a typical model description of microphysical interactions in dynamical physical systems of gases, liquids, solids, colloids, solutions, etc. Interactions between particles are described with potential energies, which result in inter-particle forces driving particles' dynamics.

19. The System is not Closed • The energy lost by a particle is not transferred to other particles, but transmitted out of the system. Similarly, a particle can gain energy from outside the system when an unlike particle moves into the neighborhood and lowers the particle's utility. • Hence, the system can change its energy only by emitting or absorbing radiation and not by changing its volume or pressure or number of particles.

20. Minimisation of Energy • The basic tendency of such a physical system is to minimize its total energy. Here, it can do that only by arranging particles into structures (clusters) that reduce the individual internal energy of as many particles as possible. In other words, interparticle forces induce particles to cluster and the stability of a cluster is determined by this force. • Hence, all we need to do is to look at the behavior of this force on the surface of a cluster to see if the surface will be stable or if it will undergo deformations and ripping.

21. A Continuous Version • Instead of counting the agents around a particular agent take the solid angle around a differential area, dA. • Take the integral of the energy along the surface and see what shapes minimise it. • There is a tendency to flatten the surface.

29. Strict improvement: The role of preferences and spaces. The formation of a solid structure

34. Evolution with indifferent movers

36. Indifference and Unlimited Moves

39. Periodic Boundaries

41. Periodic Boundaries and Long Movers

43. Clusters want to grow to reduce their surface (surface has "energetically unstable" particles) + kinetically favored energetically favored

44. The income dimension • Our next project is to examine when people also have preferences for the incomes of their neighbours. • They could prefer to be with people with similar, lower or higher income. • One possibility would be lexicographic preferences, colour first then income.

45. Income preference “everybody loves the rich”: g=number of poor neighbors

46. Race+income preference “extremes” avoid each other

47. The housing market • The previous remarks suggest that it will be the relative forces of the colour and income preferences that will emerge. • Now, the next step is to introduce prices of houses and these could be a function of the incomes of those who choose them. • What sort of clusters will emerge?

48. Market phenomena and special influences • It is widely recognised that in determining the allocation of individuals and resources in space many influences such as altruism, social or racial conformity, aspiration to public goods which may be locally provided, play an important role. • Trying to analyse the housing market without taking this sort of issue into account may result in misleading conclusions, but trying to analyse segregation without dealing with the housing market can be equally misleading.

49. Price gradient pressure Housing price utility sI<1 for rich and for poor sR<1 for white (they are richer than blacks for whom sR=1 !)

50. Racial preference Income preference sI<1 for rich sR<1 for white Housing price utility